If `n=4\ ` then `B_n` is equal to : `R^2((4-pi))/2` (b) `(R^2(4-pisqrt(2)))/2` `R^2((4sqrt(2)-pi))/2` (d) none of these

Let A_n be the area that is outside a n-sided regular polygon and inside its circumscribeing circle. Also B_n is the area inside the polygon and outside the circle inscribed in the polygon. Let R be the radius of the circle circumscribing n-sided polygon. On the basis of above information, answer the equation If n=6\ then A_n is equal to R^2((pi-sqrt(3))/2) (b) R^2((2pi-6sqrt(3))/2) R^2(pi-sqrt(3)) (d) R^2((2pi-3sqrt(3))/2)

In Fig. 15.109, the area of segment A C B is (FIGURE) (a) (pi/3-(sqrt(3))/2)\ r^2 (b) (pi/3+(sqrt(3))/2)\ r^2 (c) (pi/3-2/(sqrt(3)))\ r^2 (d) None of these

int_0^pi dx/(1-2acosx+a^2), alt1 is equal to (A) (pialog2)/4 (B) (4pi)/(2-a^2) (C) pi/(1-a^2) (D) none of these

In Fig. 15.111, if A B C is an equilateral triangle, then shaded area is equal to (FIGURE) (a) (pi/3-(sqrt(3))/4)r^2 (b) (pi/3-(sqrt(3))/2)r^2 (c) (pi/3+(sqrt(3))/4)r^2 (d) (pi/3+sqrt(3))r^2

The domain of the function f(x)=x/(sqrt(sin(lnx)-cos(lnx))),(n in Z) is (a) (e^(2npi),e^((3n+1/2)pi)) (b) (e^((2n+1/4)pi),e^((2n+5/4)pi)) (e^((2n+1/4)pi),e^((2n-3/4)pi)) (d) none of these

Let vec r=( vec axx vec b)sinx+( vec bxx vec c)cosy+2( vec cxx vec a),w h e r e vec a , vec ba n d vec c are there non-coplanar vectors. It is given that vec r is perpendicular to vec a+ vec b+ vec c , the minimum value of x^2+y^2 is equal to (A) pi^2 (B) (pi^2)/4 (C) (5pi^2)/4 (D) none of these

x=tcost ,y=t+sintdot Then (d^(2x))/(dy^2)a tt=pi/2 is (pi+4)/2 (b) -(pi+4)/2 -2 (d) none of these

int_0^oo(x dx)/((1+x)(1+x^2)) is equal to (A) pi/4 (B) pi/2 (C) pi (D) none of these"

2sin^2x+sin^2(2x)=2 , -piltxltpi then x equals (A) +- pi/2 (B) +- pi/4 (C) +-(3pi)/4 (D) none of these

If I_n=int_0^(pi/2) x^n sinx dx , then [I_4+12I_2] is equal to (A) 4pi (B) 3(pi/2)^3 (C) (pi/2)^2 (D) 4(pi/2)^3